> You can pick a point that sits on the first line to meet the carb goal. You can pick a point that sits on the second line to meet the protein goal. But you need a point that sits on both lines to hit both goals.
> How would a point sit on both lines? Well, it would be where the lines cross. Since these are straight lines, the lines cross only once, which makes sense because there’s only a single milk and bread combo that would get you to exactly five grams of carbs and seven grams of protein.
Geez. It's obvious that two straight lines can only cross once. It's not obvious that there's only one combination of discrete servings of bread and milk that can hit a particular target.
(It's so non-obvious that, in the general case, it isn't even true. Elimination might give you a row with all zeros.)
The fact that the solution is unique makes sense if you realize it must sit on these two lines. It makes far less sense to explain the fact that the two lines only cross once by channeling the external knowledge that the solution is unique. How did we learn that?
> How would a point sit on both lines? Well, it would be where the lines cross. Since these are straight lines, the lines cross only once, which makes sense because there’s only a single milk and bread combo that would get you to exactly five grams of carbs and seven grams of protein.
Geez. It's obvious that two straight lines can only cross once. It's not obvious that there's only one combination of discrete servings of bread and milk that can hit a particular target.
(It's so non-obvious that, in the general case, it isn't even true. Elimination might give you a row with all zeros.)
The fact that the solution is unique makes sense if you realize it must sit on these two lines. It makes far less sense to explain the fact that the two lines only cross once by channeling the external knowledge that the solution is unique. How did we learn that?